> That is why I have often attempted to find a common sense premise, which I often called "self-evident," such as that the area of a rectangle is proportional to the length of its side

And by the way, it is very well known that "proportional", the mathematical sense of the term, is anything but common sense. If you can solve just that one puzzle, then you will have something.:)

It seems that being able to understand proportion is unfortunately a damn good litmus test that distinguishes a mathematical student from a non-mathematical student. We generally see the failure in fractions.